The ratio of energies of two different radiations whose frequencies are $3 x 10^{14} Hz$ and $5 x 10^{14} Hz$ is ______ .

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Solution

According to Planck’s quantum theory,
Different atoms and molecules can emit or absorb energy in discrete quantities only.
The energy of the radiation absorbed or emitted is directly proportional to the frequency of the radiation.
Meanwhile, the energy of radiation is expressed in terms of frequency as,
E = hν
Where,E = Energy of the radiation, h = Planck’s constant $(6.626 \times 10^{- 34} J . s)$ , ν = Frequency of radiation
Given frequencies are $3 x 10^{14} Hz$ and $5 x 10^{14} Hz$ , the ratio of energies of two different radiations:
$\frac{E_{1}}{E_{2}} = \frac{v_{1}}{v_{2}}$
$\frac{E_{1}}{E_{2}} = \frac{3 x 10^{14} H z}{5 x 10^{14} H z}$
$\frac{E_{1}}{E_{2}} = \frac{3}{5}$
Therefore, the ratio of energies of two different radiations whose frequencies are $3 x 10^{14} Hz$ and $5 x 10^{14} Hz$ is 3:5.

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